Prediction of ocean velocities is often followed with drift prediction, a prediction of where the currents will transport a passive object from a known starting time and location, or predictions of how the ocean currents will alter the trajectory or transit time of a powered object moving through the water. Examples of usage of drift prediction include rescue and recovery, placement of instruments, and selection of a path to improve vessel fuel efficiency. Having an accurate analysis of current speed and direction is key to accurately representing drift prediction.
The inclusion of inertial oscillations in such drift predictions can adversely affect their accuracy, particularly in cases of predictions made on time scales shorter than a week. The term “inertial oscillations” is used to refer to the transverse waves in rotating fluids that are restored due to an apparent force associated with the Coriolis effect within a non-inertial reference frame fixed on a rotating planet, with the terms “inertial component” or “inertial velocity” often being used to refer to the inertial oscillation component of a velocity in a body of water due to the Coriolis effect. The restoring Coriolis effect is strongest at the poles and zero at the equator. Inertial oscillations are observed in nature, their dynamics have been described, and they continue to be the subject of investigation. If the fluid velocities are described relative to a rotating reference frame such as a latitude-longitude grid on the rotating earth, a straight-line motion relative to an inertial (non-rotating) reference frame appears to be accelerated by an apparent Coriolis force. For example, in the northern hemisphere, velocities appear to be accelerated to the right of their forward motion, while in the southern hemisphere they appear to be accelerated to the left.
Current velocities include both inertial oscillations and background flow components. The “background flow” is what remains from the velocity field after the inertial oscillations are removed. For most of the ocean basins, away from land, and under moderate winds, currents of the background flow are geostrophically balanced, with the pressure gradient due to the topography of the ocean surface balanced by an opposite Coriolis term. Both the inertial oscillations and background flow can have similar amplitudes. However, since inertial oscillations are periodic, their effect on the net long-term displacement or transport of the fluid is secondary to the effect of the non-inertial background flow, with any net transport during one-phase of the inertial oscillation being largely counterbalanced by the return flow during the opposite phase.
This process is well understood and has been the subject of a long history of theoretical studies and observational reports, for example, R. T. Pollard, On the generation by winds of inertial oscillations in the ocean, Deep-Sea Research, 17, 795-812, 1970; R. T. Pollard and R. C. Millard, Comparison between observed and simulated wind-generated inertial oscillations, Deep-Sea Research, 17, 813-821, 1970; P. Kundu, An analysis of inertial oscillations observed near Oregon coast, Journal of Physical Oceanography, 6, 879-893, 1976, and A. C. Vastano and C. N. Barron, Comparison of satellite and drifter surface flow estimates in the northwestern Gulf of Mexico, Continental Shelf Research, 14, 589-605, 1994, all of which are hereby incorporated into the present disclosure in their entirety.
An exemplary velocity field having no filtering, which includes misleading inertial oscillations as predicted, is illustrated in FIG. 1A (PRIOR ART). Each bold black arrow in FIG. 1A represents an instantaneous velocity field. For example, the circled arrow represents the instantaneous field at hour 15:00 on day 2. Collectively, the black arrows represent a time series of velocity fields sampled every three hours from the start of day 1 to the start of day 4. The line segments with arrows at the endpoints represent time windows of different durations centered on the selected velocity field, in this case hour 15:00 on day 2. The inertial period as a function of latitude is given by 11.97 hours divided by the sine of the latitude. The durations of the time windows correspond to inertial periods at different latitudes; in this case, the largest period, 35.00 hours, corresponds to the inertial period at 20° S latitude while the shortest period, 15.63 hours, corresponds to the inertial period at 50° S latitude. FIG. 1A and similar figures are used to convey the absence or implementation of different filters to remove inertial period oscillations.
In examining a time series of daily snapshots for purposes of predicting flow of possible debris, higher frequency variability in the flow field can hinder identification of the dominant flow patterns. For example, inertial oscillations can obscure the background flow and therefore can hinder interpretation of velocity field time series. Because of the small net effect of inertial oscillations on transport with duration longer than the inertial period, inertial oscillations can be misleading if an instantaneous representation of a velocity field is used to convey such drift tendencies.
Several methods have been developed to filter inertial oscillations out of a velocity time series. For example, some isolate the inertial oscillations at a single latitude using a precise filter for that single latitude or over a broad field using a broad, multiple-day time average that may span multiple inertial periods and will suppress both inertial and non-inertial variations. These methods, are not well-suited for a time series of flow fields computed to predict flow that captures variations on time scales shorter than a day.
This use of a single number for the inertial period uniquely determined at the latitude of a fixed observation such as a moored current meter has been used to isolate the inertial motion using a sharp bandpass filter as shown in, for example, Kundu, supra.
In some prior art methods, this approach has also been applied over a limited area where the range of the inertial period is small enough to be considered uniform among all points under consideration. For example, J.-H. Park and D. R. Watts, Near-inertial oscillations interacting with mesoscale circulation in the southwestern Japan/East Sea, Geophysical Research Letters, 32, L10611, doi:10.1029/2005GL022936, 2005, the entirety of which is incorporated by reference into the present disclosure, uses a narrow band filter with a single inertial period representing periods over the range of latitudes occupied by moored instruments in the Japan/East Sea.
An exemplary velocity field having a uniform filter for a central latitude that aliases inertial oscillations at different latitudes is illustrated in FIG. 1B (PRIOR ART), where the 20.87 hour window corresponding to a latitude of 35° S is in various levels of error when applied with velocities at other latitudes that have a range of inertial periods indicated by their respective time period lines and values. Thus, this method is limited in that it aliases inertial oscillations into the non-inertial flow if the span of latitudes is too large.
Still other applications have chosen to mask inertial oscillations by averaging over long time periods to suppress both inertial oscillations and all other current variations with period shorter than the averaging window. For example, L. Crosnier, B. Barnier, and A. M. Treguier, Aliasing inertial oscillations in a ⅙° Atlantic circulation model: impact on the mean meridional heat transport, Ocean Modelling, 3, 21-31, 2001, the entirety of which is incorporated by reference into the present disclosure, reports on the effects of this aliasing when examining model flow predictions over large areas; their solution is to apply a 5-day mean that damps all higher-frequency variations including inertial oscillations. The 5-day filter was also used by T. Penduff, B. Barnier, J.-M. Molines, and G. Madec, On the use of current meter data to assess the realism of ocean model simulations, Ocean Modelling, 11, 399-416, 2006, the entirety of which is incorporated by reference into the present disclosure.
An exemplary very long uniform filter that smooths all inertial oscillations and shorter-term variations is illustrated by the line segment covering a 120-hour window in FIG. 1C (PRIOR ART). This period is much longer than the range of inertial periods shown by the other time period lines and values.
The disadvantage of the long-term mean is that it eliminates both inertial and non-inertial variability over shorter time scales, and it is precisely the shorter time scales of the non-inertial velocity component that are needed in drift predictions for search and recovery or other applications. In general, errors in predicting non-inertial variations are less damaging because they are not sustained by the natural mode that propagates inertial oscillations. We are seeking a method that eliminates inertial variations while allowing other periods of variability that are more reliably forecast.
Another alternative to our methods is to strive to precisely determine the true inertial oscillations present in a drifter motion. If the inertial oscillations are correct, then they do not need to be filtered out. Such an approach is taken by T. Bengtsson, R. Milliff, R. Jones, D. Nychka, and P. P. Niiler, A state-space model for ocean drifter motions dominated by inertial oscillations, Journal of Geophysical Research, 110, C10015, doi:10.1029/2004JC002850, 2005, the entirety of which is incorporated by reference into the present disclosure, which provides a method to estimate the Coriolis parameter and atmosphere-ocean coupling coefficients from an analysis of the inertial oscillations captured by drifter trajectories. This method requires detailed observations of actual drift, and requires extensive calculations to determine how drift in a particular event reveals the coupling in that event between the ocean and atmosphere. While this approach is instructive for understanding the circumstances of a particular event of ocean coupling, it is well beyond the scope of the routine applications over broad regions envisioned for the proposed filter patent.
Thus, if inertial oscillations are the dominant source of confusion for interpreting the flow predictions, what is needed is a method for suppressing the inertial oscillations while maintaining other variations over time periods of less than a day.
What is further needed is a system that (a) combines robust applicability over a field with a large range in latitude and (b) preserves the shorter-time scale non-inertial components of the signal that are essential for flow and transport calculations in search and rescue or other wide-area ocean drift applications.
What is still further needed is a system that (a) is applicable not only at points or over small areas where the inertial period can be safely approximated as constant, but also over large areas encompassing a range of inertial period values, (b) distinguishes inertial and non-inertial velocity components, which can be used individually or in combination by subsequent drift estimates or other applications, (c) maintains shorter-time scale non-inertial components within the non-inertial velocity components, enabling drift calculations to make use of these more robust predictions while removing the less certain inertial components, (d) can be easily extended to a variety of time-filters, so long as the filter can be applied as a function of the local inertial period, (e) does not require calculation of the true contribution of inertial oscillations within a particular drift event based on specialized supporting observations and extensive calculations, and (f) can produce output that is applicable to flow and transport calculations in search and rescue or other wide-area ocean drift applications.